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I've often heard it said that almost everyone thinks that they are a better than average driver.
If this is true, it could be explained by a number of theories.
Some of these are outlined in this Wikipedia article on illusory superiorty.

I had a few questions:

Has anyone researched the actual correlation between self-perceived and other measures of driving ability?

Has anyone developed a model of the degree to which any bias is due to different causes (e.g., different values of speed versus safety; perceptual differences of others versus self; etc.)?

Expert police drivers rated themselves as superior to equally qualified drivers, to the same degree as novices, Cohen’s d = .03 ns. Despite their extensive additional training and experience, experts still appear to be as susceptible to illusions of superiority as everyone else.

Also, ratings of hazard-perception skill related to self-perceived safety after overall skill was controlled for. We suggest that although drivers appear to appreciate the role of hazard perception in safe driving, any safety benefit to be derived from this appreciation may be undermined by drivers' inflated opinions of their own hazard-perception skill. We also tested the relationship between illusory beliefs about driving skill and risk taking and looked at ways of manipulating drivers' illusory beliefs.

Although young drivers' estimates of accident involvement in the next year were higher than those of older drivers, young drivers gave lower ratings of accident risk for specific driving situations which demanded fast driving reflexes or substantial vehicle-handling skills. Young drivers rated their own risk of an accident and driving abilities as being the same as for older drivers. However, they saw their peers as being significantly higher at risk and having poorer abilities than themselves.

No relationship was found between confidence and adverse driving events or driving performance. Understanding the relationship of confidence and self-rating of driving ability to driving patterns, adverse events and driving performance may provide additional insights into identifying older drivers at increased risk for problems and formulating intervention strategies to help lower risk.

Overall it appears that young drivers are likely to have excessively high confidence in their own ability. There isn't much evidence to suggest that higher or lower confidence actually correlates with a specific skill level. Older drivers seem to have better driving skill and less overconfidence, but I have not seen results controlling for age and correlating driving ability with confidence except the study on older drivers which showed no correlation.

We examined whether people recognized that others might disagree with
their high self assessments of driving ability, and, if so, why.
Participants in four experiments expressed a belief that others would
assess them as worse drivers than they assessed themselves. This
difference appears to be caused by participants’ use of their own,
idiosyncratic definition of driving ability. In Experiments 2 and 3
participants reported that others would supply similar assessments of
their ability when the skill was less ambiguous. Results of Experiment
4 indicate that participants recognize that there may be more than
one way to view driving performance. Participants appear aware that
others likely disagree with their self-assessment of driving ability
due to differences in how others define driving ability

Thus, the authors take seriously the concept of idiosyncratic definitions of ability. However, they acknowledge that such a perspective does not explain the whole effect, whereby in the discussion they write:

While previous research (Dunning et al., 1989; Dunning et al., 1995;
Dunning & McElwee, 1995; Dunning et al., 1989; Hayes & Dunning, 1997;
Santos-Pinto & Sobel, 2005) and the current studies suggest that
people might assess themselves as above average because they focus on
their idiosyncratic definitions of ability, it is important to note
that this cannot explain the bias in full. Even though the average
participant thought that others would have a lower view of their
ability, participants still thought that others would view them as
being an above average driver, typically scoring them around the 60
th percentile or higher. Unfortunately, we cannot determine how
biased the participants in the present studies were since their
actual ability level was not measured (e.g., Kwan et al., 2004). In
fact, it is possible that the young adults in our study were actually
more skilled than average.